in Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence (2017, August)

Belief change and non-monotonic reasoning are usually viewed as two sides of the same coin, with results showing that one can formally be defined in terms of the other. In this paper we show that we can ... [more ▼]

Belief change and non-monotonic reasoning are usually viewed as two sides of the same coin, with results showing that one can formally be defined in terms of the other. In this paper we show that we can also integrate the two formalisms by studying belief change within a (preferential) non-monotonic framework. This integration relies heavily on the identification of the monotonic core of a non-monotonic framework. We consider belief change operators in a non-monotonic propositional setting with a view towards preserving consistency. These results can also be applied to the preservation of coherence—an important notion within the field of logic-based ontologies. We show that the standard AGM approach to belief change can be adapted to a preferential non-monotonic framework, with the definition of expansion, contraction, and revision operators, and corresponding representation results. Surprisingly, preferential AGM belief change, as defined here, can be obtained in terms of classical AGM belief change. [less ▲]

In access control frameworks with the possibility of delegating permissions and administrative rights, delegation chains can form. There are di erent ways to treat these delegation chains when revoking ... [more ▼]

In access control frameworks with the possibility of delegating permissions and administrative rights, delegation chains can form. There are di erent ways to treat these delegation chains when revoking rights, which give rise to di erent revocation schemes. Hagstr om et al. [11] proposed a framework for classifying revocation schemes, in which the di erent revocation schemes are de ned graph-theoretically. At the outset, we identify multiple problems with Hagstr om et al.'s de nitions of the revocation schemes, which can pose security risks. This paper is centered around the question how one can systematically ensure that improved de nitions of the revocation schemes do not lead to similar problems. For this we propose to apply the axiomatic method originating in social choice theory to revocation schemes. Our use of the axiomatic method resembles its use in belief revision theory. This means that we de ne postulates that describe the desirable behaviour of revocation schemes, study which existing revocation frameworks satisfy which postulates, and show how all de ned postulates can be satis ed by de ning the revocation schemes in a novel way. [less ▲]

Recent extensions of description logics for dealing with different forms of non-monotonic reasoning don’t take us beyond the case of defeasible subsumption. In this paper we enrich the DL EL⊥ with a ... [more ▼]

Recent extensions of description logics for dealing with different forms of non-monotonic reasoning don’t take us beyond the case of defeasible subsumption. In this paper we enrich the DL EL⊥ with a (constrained version of) a typicality operator •, the intuition of which is to capture the most typical members of a class, providing us with the DL EL•⊥. We argue that EL•⊥ is the smallest step one can take to increase the expressivity beyond the case of defeasible subsumption for DLs, while still retaining all the rationality properties an appropriate notion of defeasible subsumption is required to satisfy, and investigate what an appropriate notion of non-monotonic entailment for EL•⊥ should look like. [less ▲]

Proceedings of the 4th International Workshop on Defeasible and Ampliative Reasoning (DARe-17), co-located with the 14th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR-17 ... [more ▼]

Proceedings of the 4th International Workshop on Defeasible and Ampliative Reasoning (DARe-17), co-located with the 14th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR-17). Espoo, Finland, July 3—6, 2017. [less ▲]

We consider the problem of obtaining coherence in a propositional knowledge base using techniques from Belief Change. Our motivation comes from the field of formal ontologies where coherence is ... [more ▼]

We consider the problem of obtaining coherence in a propositional knowledge base using techniques from Belief Change. Our motivation comes from the field of formal ontologies where coherence is interpreted to mean that a concept name has to be satisfiable. In the propositional case we consider here, this translates to a propositional formula being satisfiable. We define belief change operators in a framework of nonmonotonic preferential reasoning.We show how the introduction of defeasible information using contraction operators can be an effective means for obtaining coherence. [less ▲]

We propose a method for an agent to revise its incomplete probabilistic beliefs when a new piece of propositional information is observed. In this work, an agent’s beliefs are represented by a set of ... [more ▼]

We propose a method for an agent to revise its incomplete probabilistic beliefs when a new piece of propositional information is observed. In this work, an agent’s beliefs are represented by a set of probabilistic formulae – a belief base. The method involves determining a representative set of ‘boundary’ probability distributions consistent with the current belief base, revising each of these probability distributions and then translating the revised information into a new belief base. We use a version of Lewis Imaging as the revision operation. The correctness of the approach is proved. The expressivity of the belief bases under consideration are rather restricted, but has some applications. We also discuss methods of belief base revision employing the notion of optimum entropy, and point out some of the benefits and difficulties in those methods. Both the boundary distribution method and the optimum entropy method are reasonable, yet yield different results. [less ▲]

In this paper we consider the problem of obtaining coherence in a propositional knowledge base using techniques from Belief Change. Our motivation comes from the field of formal ontologies where coherence ... [more ▼]

In this paper we consider the problem of obtaining coherence in a propositional knowledge base using techniques from Belief Change. Our motivation comes from the field of formal ontologies where coherence is interpreted to mean that a concept name has to be satisfiable. [less ▲]

in Proceedings of the 22nd European Conference on Artificial Intelligence (ECAI-16) (2016)

We propose a method for an agent to revise its incomplete probabilistic beliefs when a new piece of propositional information is observed. In this work, an agent’s beliefs are represented by a set of ... [more ▼]

We propose a method for an agent to revise its incomplete probabilistic beliefs when a new piece of propositional information is observed. In this work, an agent’s beliefs are represented by a set of probabilistic formulae – a belief base. The method involves determining a representative set of ‘boundary’ probability distributions consistent with the current belief base, revising each of these probability distributions and then translating the revised information into a new belief base. We use a version of Lewis Imaging as the revision operation. The correctness of the approach is proved. An analysis of the approach is done against six rationality postulates. The expressivity of the belief bases under consideration are rather restricted, but has some applications. We also discuss methods of belief base revision employing the notion of optimum entropy, and point out some of the benefits and difficulties in those methods. Both the boundary distribution method and the optimum entropy methods are reasonable, yet yield different results. [less ▲]

Proceedings of the International Workshop on Defeasible and Ampliative Reasoning (DARe-16), co-located with the 22th European Conference on Artificial Intelligence (ECAI 2016). The Hague, Holland, August ... [more ▼]

Proceedings of the International Workshop on Defeasible and Ampliative Reasoning (DARe-16), co-located with the 22th European Conference on Artificial Intelligence (ECAI 2016). The Hague, Holland, August 29, 2016. [less ▲]

Proceedings of the International Workshop on Defeasible and Ampliative Reasoning (DARe-15), co-located with the 24th International Joint Conference on Artificial Intelligence (IJCAI 2015). Buenos Aires ... [more ▼]

Proceedings of the International Workshop on Defeasible and Ampliative Reasoning (DARe-15), co-located with the 24th International Joint Conference on Artificial Intelligence (IJCAI 2015). Buenos Aires, Argentina, July 27, 2015. [less ▲]

In recent years, various approaches have been developed for representing and reasoning with exceptions in OWL. The price one pays for such capabilities, in terms of practical performance, is an important ... [more ▼]

In recent years, various approaches have been developed for representing and reasoning with exceptions in OWL. The price one pays for such capabilities, in terms of practical performance, is an important factor that is yet to be quantified comprehensively. A major barrier is the lack of naturally occurring ontologies with defeasible features - the ideal candidates for evaluation. Such data is unavailable due to absence of tool support for representing defeasible features. In the past, defeasible reasoning implementations have favoured automated generation of defeasible ontologies. While this suffices as a preliminary approach, we posit that a method somewhere in between these two would yield more meaningful results. In this work, we describe a systematic approach to modify real-world OWL ontologies to include defeasible features, and we apply this to the Manchester OWL Repository to generate defeasible ontologies for evaluating our reasoner DIP (Defeasible-Inference Platform). The results of this evaluation are provided together with some insights into where the performance bottle-necks lie for this kind of reasoning. We found that reasoning was feasible on the whole, with surprisingly few bottle-necks in our evaluation. [less ▲]

Propositional Typicality Logic (PTL) is a recently proposed logic, obtained by enriching classical propositional logic with a typicality operator. In spite of the non-monotonic features introduced by the ... [more ▼]

Propositional Typicality Logic (PTL) is a recently proposed logic, obtained by enriching classical propositional logic with a typicality operator. In spite of the non-monotonic features introduced by the semantics adopted for the typicality operator, the obvious Tarskian definition of entailment for PTL remains monotonic and is therefore not appropriate. We investigate different (semantic) versions of entailment for PTL, based on the notion of Rational Closure as defined by Lehmann and Magidor for KLM-style conditionals, and constructed using minimality. Our first important result is an impossibility theorem showing that a set of proposed postulates that at first all seem appropriate for a notion of entailment with regard to typicality cannot be satisfied simultaneously. Closer inspection reveals that this result is best interpreted as an argument for advocating the development of more than one type of PTL entailment. In the spirit of this interpretation, we define two primary forms of entailment for PTL and discuss their advantages and disadvantages. [less ▲]